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The difference between primal and dual are that primal means an essential, or fundamental of an aspect where as dual means consisting of two parts or elements. Primal is one, dual is two.

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Is dual of the dual equivalent to primal?

Yes, in linear programming, the dual of the dual problem is equivalent to the primal problem. This relationship is a fundamental concept in the theory of duality, which states that every linear program has a corresponding dual program, and taking the dual twice will return you to the original primal formulation. This equivalence is useful for understanding the solutions and relationships between primal and dual problems.


What are the rules for converting a primal problem into its dual?

To convert a primal linear programming problem into its dual, the following rules apply: If the primal is a maximization problem with constraints in the form of inequalities (≤), the dual will be a minimization problem with constraints in the form of inequalities (≥). The coefficients of the objective function in the primal become the right-hand side constants in the dual, while the right-hand side constants of the primal become the coefficients in the dual's objective function. The primal's variables correspond to the dual's constraints and vice versa, effectively switching their roles. Additionally, if the primal has ( m ) constraints and ( n ) variables, the dual will have ( n ) constraints and ( m ) variables.


How we convert the primal into dual problem in lpp?

To convert a primal linear programming problem into its dual, we first identify the primal's objective function and constraints. If the primal is a maximization problem with ( m ) constraints and ( n ) decision variables, the dual will be a minimization problem with ( n ) constraints and ( m ) decision variables. The coefficients of the primal objective function become the right-hand side constants in the dual constraints, while the right-hand side constants of the primal constraints become the coefficients in the dual objective function. Additionally, the direction of inequalities is reversed: if the primal constraints are ( \leq ), the dual will have ( \geq ) constraints, and vice versa.


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